So far, we have seemingly demonstrated an universal positive correlation between the \(\mathcal {NC}\)\(_1\)  and transferability. However, does the increase for the \(\mathcal {NC}\)\(_1\)  of learned features always lead to improved model transferability? To more comprehensively characterize the relationship between \(\mathcal {NC}\)\(_1\)  and transferability, we pre-train ResNet50 models on the Cifar-100 dataset using different levels of data augmentations and adversarial training [1]}, [2]}, [3]} strength,We use 5 levels of data augmentations, each level represents adding one additional type of augmentation, e.g., Level 1 means Normalization, level 2 means Normalization + RandomCrop, etc. For adversarial training strength, we follow the framework in [1]} and consider 5 different attack sizes. Please refer to Appendix  for more details. and then test the transfer accuracy on the Cifar-10 dataset. The results are shown in fig:algadvncfail. Our observation is that the positive relationship between the \(\mathcal {NC}\)\(_1\)  on the source dataset and the transfer accuracy only holds up to a certain threshold.The work [5]} studied the transferability based upon a notion called class separation, which is similar to \(\mathcal {NC}\)\(_1\) . However, the work only studied the relationship within a limited range of class separation, which excludes the case of zero class separation. If the \(\mathcal {NC}\)\(_1\)  metric is larger than a certain threshold, the transfer accuracy decreases as the \(\mathcal {NC}\)\(_1\)  increases.
